An official website of the United States government
We consider the problem of active learning in the context of spatial sampling for boundary estimation, where the goal is to estimate an unknown boundary as accurately and quickly as possible. We present a finite-horizon search procedure to optimally minimize both the final estimation error and the distance traveled for a fixed number of samples, where a tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem.
more »
« less
A finite-horizon approach to active level set estimation
We consider the problem of active learning for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible. We present a finite-horizon search procedure to perform LSE in one dimension while optimally balancing both the final estimation error and the distance traveled during active learning for a fixed number of samples. A tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem. We then show how this approach can be used to perform level set estimation in two dimensions, under some additional assumptions, under the popular Gaussian process model. Empirical results on synthetic data indicate that as the cost of travel increases, our method's ability to treat distance nonmyopically allows it to significantly improve on the state of the art. On real air quality data, our approach achieves roughly one fifth the estimation error at less than half the cost of competing algorithms.
more »
« less
- Award ID(s):
- 2136228
- PAR ID:
- 10579194
- Publisher / Repository:
- AIMS
- Date Published:
- Journal Name:
- Foundations of Data Science
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 2639-8001
- Page Range / eLocation ID:
- 0 to 0
- Subject(s) / Keyword(s):
- Adaptive sampling, autonomous systems, dynamic programming, Gaussian processes, level set estimation, mobile sensors
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper focuses on the system identification of an important class of nonlinear systems: nonlinear systems that are linearly parameterized, which enjoy wide applications in robotics and other mechanical systems. We consider two system identification methods: least-squares estimation (LSE), which is a point estimation method; and set-membership estimation (SME), which estimates an uncertainty set that contains the true parameters. We provide non-asymptotic convergence rates for LSE and SME under i.i.d. control inputs and control policies with i.i.d. random perturbations, both of which are considered as non-active-exploration inputs. Compared with the counter-example based on piecewise-affine systems in the literature, the success of non-active exploration in our setting relies on a key assumption about the system dynamics: we require the system functions to be real-analytic. Our results, together with the piecewise-affine counter-example, reveal the importance of differentiability in nonlinear system identification through non-active exploration. Lastly, we numerically compare our theoretical bounds with the empirical performance of LSE and SME on a pendulum example and a quadrotor example.more » « less
-
Abstract To navigate through the environment, humans must be able to measure both the distance traveled in space, and the interval elapsed in time. Yet, how the brain holds both of these metrics simultaneously is less well known. One possibility is that participants measure how far and how long they have traveled relative to a known reference point. To measure this, we had human participants (n = 24) perform a distance estimation task in a virtual environment in which they were cued to attend to either the spatial or temporal interval traveled while responses were measured with multiband fMRI. We observed that both dimensions evoked similar frontoparietal networks, yet with a striking rostrocaudal dissociation between temporal and spatial estimation. Multivariate classifiers trained on each dimension were further able to predict the temporal or spatial interval traveled, with centers of activation within the SMA and retrosplenial cortex for time and space, respectively. Furthermore, a cross-classification approach revealed the right supramarginal gyrus and occipital place area as regions capable of decoding the general magnitude of the traveled distance. Altogether, our findings suggest the brain uses separate systems for tracking spatial and temporal distances, which are combined together along with dimension-nonspecific estimates.more » « less
-
We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be prohibitive, and it may be imperative for them to use sparsification techniques. While most existing work on sparsified mean estimation is agnostic to the characteristics of the data vectors, in many practical applications such as federated learning, there may be spatial correlations (similarities in the vectors sent by different nodes) or temporal correlations (similarities in the data sent by a single node over different iterations of the algorithm) in the data vectors. We leverage these correlations by simply modifying the decoding method used by the server to estimate the mean. We provide an analysis of the resulting estimation error as well as experiments for PCA, K-Means and Logistic Regression, which show that our estimators consistently outperform more sophisticated and expensive sparsification methods.more » « less
-
State estimation (SE) is an important energy management system application for power system operations. Linear state estimation (LSE) is a variant of SE based on linear relationships between state variables and measurements. LSE estimates system state variables, including bus voltage magnitudes and angles in an electric power transmission network, using a network model derived from the topology processor and measurements. Phasor measurement units (PMUs) enable the implementation of LSE by providing synchronized high-speed measurements. However, as the size of the power system increases, the computational overhead of the state-of-the-art (SOTA) LSE grows exponentially, where the practical implementation of LSE is challenged. This paper presents a distributed linear state estimation (D-LSE) at the substation and area levels using a hierarchical transmission network topology processor (H-TNTP). The proposed substation-level and area-level D-LSE can efficiently and accurately estimate system state variables at the PMU rate, thus enhancing the estimation reliability and efficiency of modern power systems. Network-level LSE has been integrated with H-TNTP based on PMU measurements, thus enhancing the SOTA LSE and providing redundancy to substation-level and area-level D-LSE. The implementations of D-LSE and enhanced LSE have been investigated for two benchmark power systems, a modified two-area four-machine power system and the IEEE 68 bus power system, on a real-time digital simulator. The typical results indicate that the proposed multilevel D-LSE is efficient, resilient, and robust for topology changes, bad data, and noisy measurements compared to the SOTA LSE.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/fods.2024050
